Question: Simplify the following expression: $z = \dfrac{-18n + 48}{-48n - 42}$ You can assume $n \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-18n + 48 = - (2\cdot3\cdot3 \cdot n) + (2\cdot2\cdot2\cdot2\cdot3)$ The denominator can be factored: $-48n - 42 = - (2\cdot2\cdot2\cdot2\cdot3 \cdot n) - (2\cdot3\cdot7)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $z = \dfrac{(6)(-3n + 8)}{(6)(-8n - 7)}$ Dividing both the numerator and denominator by $6$ gives: $z = \dfrac{-3n + 8}{-8n - 7}$